lean_workbook_plus_7809

⚠️ Retired — specification defect

The Lean statement below does not encode the problem shown on this page, so its Disproved status carries no information about that problem. Do not import this node or use it as a dependency.

Let $p$ be a prime such that $p \equiv 3 \pmod 4$ . Prove that we can't partition the numbers $a,a+1,a+2,\cdots,a+p-1$ in two sets such that product of members of the sets be equal.

Why this node was retired

The posted statement is

theorem lean_workbook_plus_7809 (p a : ℕ) (hp : p.Prime) (hp1 : p ≡ 3 [ZMOD 4]) :
    ¬ (∃ A : Finset ℕ, ∃ B : Finset ℕ,
       A ∪ B = Finset.Icc a (a + p - 1) ∧
       A.prod id = B.prod id)   :=  by sorry

Add Disjoint A B to the partition conditions; retain their union as the consecutive interval.

The recorded counterexample refutes the statement as encoded. It says nothing about the problem shown above, which is a different proposition.

Proposed corrected statement

Add Disjoint A B to the partition conditions; retain their union as the consecutive interval.

Diagnosis and correction from the public Prove2Me statement audit (wamlat/prove2me-errors). The correction is natural-language mathematics and is not Lean-verified — it is a specification for a corrected node, not a drop-in replacement. No corrected replacement node exists yet.